document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=456904>Question 456904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the equation of the ellipse with foci (0, 4), (0, -4) and vertices (0, 8), (0, -8)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #313721 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=313721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the equation of the ellipse with foci (0, 4), (0, -4) and vertices (0, 8), (0, -8)<BR>\n" );
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document.write( "Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.<BR>\n" );
document.write( "The difference between the two forms is the interchange of a^2 and b^2<BR>\n" );
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document.write( "Because the given x-coordinates of foci and vertices are the same at x=0, ellipse has a vertical major axis.<BR>\n" );
document.write( "length of major axis=16=2a<BR>\n" );
document.write( "center at (0,0) (midpoints of vertices and foci)<BR>\n" );
document.write( "a=8<BR>\n" );
document.write( "a^2=64<BR>\n" );
document.write( "c=half the distance between foci=8/2=4<BR>\n" );
document.write( "c^2=16<BR>\n" );
document.write( "c^2=a^2-b^2<BR>\n" );
document.write( "b^2=a^2-c^2=64-16=48<BR>\n" );
document.write( "b&#8730;48=6.93..<BR>\n" );
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document.write( "Equation:(x-0)^2/48+(y-0)^2/64=1<BR>\n" );
document.write( "=x^2/48+y^2/64=1<BR>\n" );
document.write( "see graph below as a visual check on the answers. note the center and end points of the ellipse.<BR>\n" );
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document.write( "y=(64-64(x^2)/48)^.5\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%2864-64%28x%5E2%29%2F48%29%5E.5%2C-%2864-64%28x%5E2%29%2F48%29%5E.5%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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